The Casimir energy anomaly for a point interaction

Abstract

The Casimir energy for a massless, neutral scalar field in presence of a point interaction is analyzed using a general zeta-regularization approach developed in earlier works. In addition to a regular bulk contribution, there arises an anomalous boundary term which is infinite despite renormalization. The intrinsic nature of this anomaly is briefly discussed.

arXiv comment5 pages. To appear in the special issue of Mod.Phys.Lett.A containing the Proceedings of the 4th Casimir Symposium (St.Petersburg, June 24-28, 2019)

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• Vacuum polarization with zero-range potentials on a hyperplane
• A note on "Algebraic approach to Casimir force between two $\delta$-like potentials" (K. Ziemian, Ann. Henri Poincaré, Online First, 2021)